第3章共價鍵理論和雙原子分子結(jié)構

物理化學

3-1Covalencebond 2011-11- 復旦大學化學 物理化學TheAtomandtheMolecule.April1916.J.Am.Chem.Soc.,38,2011-11- 復旦大學化學 物理化學

3-1CovalencebondCovalentandIonicContourmapsofthemolecularchargedistributionsofN2andLiFattheirequilibriuminternuclearseparations2011-11- 復旦大學化學 物理化學

3-1CovalencebondTheHamiltonianofH2??1?

?1?2

?2

?2?1

1?1?1

+1

(R,r)

Eψ(R,r) ψ a

12 TheTheunderlyingphysicallawsnecessaryforthemathematicaltheoryof…thewholeofchemistryarethuscompleyknown,andthedifficultyisonlythattheexactapplicationoftheselawsleadstoequationsmuchtoocomplicatedtobesoluble.2011-11- 復旦大學化學 物理化學

3-1Covalencebond??1?

?1?2

?2

?2?1

1?1?1

+1

(R,r)

Eψ(R,r)

B.O.

a

12112

r

?? ??2 12

??2??2

?

?

?

+

?ψ(r)?

E(R)ψ(r)2011-11- 復旦大學化學 物理化學

3-1Covalencebond?? ??2 12

??2??2

?

?

?

+

?ψ(r)?

E(R)ψ(r)Separate??1?2?1?1

??(r)

2 2

?2011-11- 復旦大學化學 物理化學

3-1Covalencebond?? ??2 12

??2??2

?

?

?

+

?ψ(r)?

E(R)ψ(r)

ψ1=ψa(1)ψbψ2=ψa(2)ψb物理化學

3-1CovalencebondEE=∫*Hψd?∫ψ*ψd=∫(C1ψ)?∫(C11+C dτ =∫ψiψjdτS11=S22=S=H11=HHij =∫ψi?ψjdτH12=H21E(C2E(C2+C2+2CC12 )=C2H1+C2H2+2CC ?E=E(C +C1 )=C1+C ?E=E(C2C1S12)C2H222011-11- 復旦大學化學 物理化學

3-1Covalencebond?E=

(H11

?E)C1+(H12

?ES12)C2=

?E=

(H12

?ES12

+(H22?E)C2=

H11?HH11?H12?ESH12?ESH22?= =H

+H

=H

?H 1

S12

1

S122+2S2+2S

ψ1+ψ

ψII

ψ1?ψ2?2S2?2S物理化學

3-1Covalencebond

=∫ψ

=∫∫

1dτ2

S?= ?1+S?=?

R2?23?3?

(2)??a

Q 1??1??2?R?e=∫∫?a(1)?b(2)[?a(1)+?b(2)+?Q 1??1??2?R?e=EH+EH+H

=∫ψ1?ψ2dτ=∫∫?a(1)?b(2)??a(2)?b(1)dτ1dτ=∫∫?a(1)?b(2)[?

a(2)

?b(1)

?ab(1,2)]?a(2)?b(1)dτ1dτS=E+2S=E+

A?? A?? 2R???3?eSE+EI=EI=H11+H1+=2H+Q+1+SE=H11?H1?=2H+Q?1?S2011-11- 復旦大學化學 EI=HEI=H+H1+=2H+Q+1+S

3-1Covalencebondrr0=0.87De=E=H11?H1?=2H+Q?1?SShoujingr0=0.74物理化學 3-1Covalencebond物理化學

3-1CovalencebondDe=r0=0.742r0=0.742De =4.741960 采用50個變分參數(shù),應用計算機的結(jié)2011-11- 復旦大學化學 物理化學

3-1CovalencebondElectronicρ2

22?22? b

(2

?a

(2

(1)2dτ11 [?2(2)+?2(2)+11

(2) 222222

ψ1,22dτ

abab22

?

2?? S1 S1

?2?22??

1S

abρ經(jīng)

=?

+?ab2011-11- 復旦大學化學 ab物理化學

Covalencebond ?

]>aS1經(jīng) aS1 ?

?1]<aSS1經(jīng)aSS1

TheNatureoftheCovalentBond2011-11- 復旦大學化學 物理化學

CovalencebondAcontourmapoftheelectrondensitydistribution(orthemolecularchargedistribution)forH2inanecontainingthenuclei.Alsoshownisaprofileofthedensitydistributionalongtheinternuclearaxis.Theinternuclearseparationis1.4au.Thevaluesofthecontoursincreaseinmagnitudefromtheoutermostoneinwardstowardsthenuclei.Thevaluesofthecontoursinthisandallsucceedingdiagramsaregiveninau;1au=e/ao3=6.749e/?3.2011-11- 復旦大學化學 物理化學

CovalencebondAseriesofelectrondensitycontourmapsillustratingthechangesintheelectronchargedistributionduringtheapproachoftwoHatomstoformH2.TheinternucleardistanceRinunitsofauisindicatedbeneatheach2011-11- 復旦大學化學 物理化學

Covalencebond distribution(molecularminusatomic)fortheapproachoftwoHatoms.Thesemapsindicatethechangesintheatomicdensitiescausedbytheformationofamolecule.2011-11- 復旦大學化學 物理化學

CovalencebondThespinof

(1,2)

2+η44=()α(22+2+2+

ψ1+ψ

=?a(1)?b(2)+?a(2)?b

'α)()α(2)β ?ψ

?(1)?(2)??(2)?

122?122?2?

η2=β(1)β2011-11- 復旦大學化學 a物理化學a

Covalencebond2+22+2S

(1)?b

(2)

?a(2)?b

(1)][α(1)

(

?α(2)

(1)]=(1=

(1)?b

(

??

(2)?b

(1)][α(1)

(

+α(2)

(1)2?2S2?2S=

(2)?

(2)?b

(1)α2?2S12a=2?2S12a=

(2

??

(2)?b

(1)

(2aa12?2S12?2Sab物理化學

2011-11- 復旦大學化學 物理化學

CovalencebondSummaryofValenceBondTheoryandItsThesetwoelectronsmusthaveopposite

=

a(1)?

(2)

?a(2)?

(1)

(1)

(2)?

(2)ff

(1)1s133PrincipleofumOverlap:thestrengththebonddependsontheextentofoverlapofthechargecloudsonthetwoatoms.

5fd57zf37z2011-11- 復旦大學化學 物理化學

CovalencebondTheApplicationforSome2 2NNNN2011-11- 復旦大學化學 物理化學

CovalencebondCarryoutalinearvariationcalculationforaparticleofmassminone-dimensionalinfinitepotentialwellofwidthl. ψ1lx

ψ2

l2

astrialComparetheresultwiththeexactstate2011-11- 復旦大學化學 物理化學

MolecularOrbitalMolecularMolecularOrbitalTheHamiltonianforH2+inatomic?

?1?2

?? ??

1???b ??b

?

?1?22a

B.O.11?1

1901–19Americanchemist.OneofthefewrecipientsoftwoNobelprizes.Hispaper“TheNatureoftheChemicalBondandtheStructureofMoleculesandCrystals”wonhimthe1954NobelPrizeinchemistry.Wonthepeaceprizeinb2011-11- 復旦大學化學 π物理化學π

MolecularOrbital?

?1?2?

ψ

=twolimit ?

?1?2?

ψ

e?

=πTheSpatialwavefunctiononeachoftwoHatomsformslinearcombinationsπTheSpatialwavefunctiononeachoftwoHatomsformslinearcombinationsEE∫(C1?a+C2?b?(C1?a+C2?b∫C +C?)2 τE(C2+C2+2CC12 )=C2H +C2H +2CC 2011-11- 復旦大學化學 物理化學

MolecularOrbitalE(C1+E(C1+C2Sab)=C1Haa+C2HabE(C2+C1Sab)=C2Hbb+C1HabE((Haa?E)C1+(Hab?ESab)C2=(Hab?ESab)C1+(Hbb?E)C2=Haa?

Hab

? =Hab

?

Hbb? =

+

=

?

Thenormalized2+2Sab2+2Sab

1?

wavefunctionsψI

?a+

ψII

?a?

2?2011-11-2?物理化學

MolecularOrbital

=Haa

+H

=H

?H? 1?

Sab

1

Sab

=∫

=?1+R?

R2?3

ThewavefunctionsfromtwoHatomsarenotorthogonalandtheoverlapintegralisafunctionoftheinternucleardistance.Haa

=∫

??adτ

=∫?

1?2?? ?

?1

?a

EHJa a

ab

J

11Hab

=∫?

??b

?aa∫

1?2?1?? ?

?

REHSabKβ

2011-11- 復旦大學化學 物理化學

MolecularOrbital =H

+Hab =

+J+

H

H

J1+

1+

1

1 =

+

=α+

≈α+

1+ 1+ =

?

=α?

≈α?1?

1?

DiagramofH2+energy

2PotentialenergysurfaceforH22011-11- 復旦大學化學 物理化學

MolecularOrbital2011-11- 復旦大學化學 物理化學

MolecularOrbitalElectronic

1?2?22 +2

no-

ψI

22+

ρI=ψ

=2

2Sab

+?

+

a?bab12ab122011-11- 復旦大學化學 物理化學

MolecularOrbitalElectronic

1?2?2no-

ab ab2?2?

?a?

ρII

=ψ

2 2?

+?

?

a?b 2011-11- 復旦大學化學 物理化學

MolecularOrbital NatureofCovalence RedistributionofelectrondensityloweringthesystemenergymakesthemoleculestableIntomicattractionorrepulsionisdeterminedbythechangeoftheelectrondensityInabondingortital,thenucleiareattractedtotheaccumulationofelectrondensityintheinternuclearregion.Inanantibondingortital,thenucleiareattractedtoanaccumulationofelectrondensityoutsidetheinternuclearregion ?12+?22?± ?12+?222011-11- 復旦大學化學 物理化學

3-2MolecularOrbitalOutlineOutlineofMolecular-OrbitalTheHamiltonianofa 2

Zi

1

ZaZH

2

2

2i1

i

a1

ai

j

a abΨψ1ψ2ψMolecularnn

12

Zi1 mn mn

i1

a a

j

ij

1 mZ

1E

b

2

j

2011-11- 復旦大學化學 物理化學

3-2MolecularOrbitaln i12imaZrn1jr2nE12 Z Z1Rab12 j ψ1ψ2ψrij Uri

ψj

ψjdτ

nnnn

jnn

nψn

j nn1ψψdτdτnn

j i

j

i

j

ψ=ψ

???12 ???12 ?m2Z ia= +U(ri)?ψi=Eiψ?1

ZaZb1 n2 2 2

i

ba

j22011-11- 復旦大學化學 2物理化學

3-2MolecularOrbitalBuildingPrincipleinMolecular---by???12?2i∑a=1mrZi+???12?2i∑a=1mrZi+U(r) =Eψi?i

ψψi=∑Cij?jj=1nWhisWhisthe2011-11- 復旦大學化學 物理化學

3-2MolecularOrbital

Zi ???2?i?

?a=1

?

=Eiψ

ψi

∑Cij?jj=1Amouldingmoleculeψ

Ea

Whichkindsofatomicorbitalscanbeused(Haa

?E)Ca+(Hab

?ESab)Cb=

constructthe(Hab

?ESab

+(Hbb?E)Cb=

Haa?

Hab

? =

Haa

?

Hbb

?

Sab=Hab

?

Hbb?

Hab

=

=∫

??bdτ2011-11- 復旦大學化學 物理化學

3-2MolecularOrbitalαa?

β?ES=β?

αb?2S=2E=2

+αb

+4β2[h=[2

?

+4β

?

?αb

)]>abaE αaaba

E

=αb?bE=αa+αb?b

?h)

E1=αa+2=[(αa?αb2

+4

2]>α =α = ?bα物理化學

3-2MolecularOrbital[2OnlyAOsofreasonablesimilarenergiescontributesubstantiallytoagivenMO.(energycloser)[2αa>>

h=2

+4β

?

a?α

zAllorbitalsoftheappropriatesymmetrycontributetoazmolecularorbital ??bzThegreattheoverlap,thegreatthebondstrength(principleofzumxβ=∫?a??bdτ=EbSab+2011-11- 復旦大學化學 物理化學

3-2MolecularOrbital+σ++++±++++m=+++++±++++2011-11- 復旦大學化學 物理化學++π++±

3-2MolecularOrbital+++++m=++++++++++±+++++2011-11- 復旦大學化學 物理化學

3-2MolecularOrbital++++δ++m= ++2011-11- 復旦大學化學 ++物理化學

3-2MolecularOrbitalTheThesymbolofmolecularHomonuclearDiatomic

σ

σσ 2σσ

π2

Heteronuclearatomic 2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicDiatomicEigenenergyofatomicorbitalHBCNOF2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicconfiguraioordemagnetisH2σ11/2paramagnetisHσ11diamagnetisHe2σ (σ*)1 11/2paramagnetisHσ (σ*)1 10diamagnetisLi2KKσ21/2paramagnetisLi2KKσ21diamagnetisBe2KKσ (σ*)2 21/2paramagnetisBeKKσ (σ*)2 20diamagnetisBKKσ (σ )2π π2 2 2 21paramagnetisCKKσ (σ )2π π2 2 2 22diamagnetisNKKσ (σ )2π π σ2 2 2 2 23diamagnetisOKKσ (σ )2π π σ π* π*2 2 2 2 2 2 22paramagnetisFKKσ (σ )2π π σ π* π*2 2 2 2 2 2 21diamagnetis2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomic2011-11- 復旦大學化學 物理化學 3-3thestructureofdiatomic物理化學

3-3thestructureofdiatomic 2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicSymbolSymbolofmolecularTheenergyforagivenmolecularelectronicconfigurationofadiatomicmoleculeisdependentupontheangularmomentumstateofthesysteminsuchthesamewayasinthecaseforatoms.OrbitalOneelectronatommoleculelλOrbitalOneelectronatommoleculelλ l(l+1)l=0(s),1(p),2(d),3(f λ(λ+1)λ=0(σ),1(π),2(δlλlz=mlml=l,l?1,,?λz=mλmλ=λ,?2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicLLLL L(L+L=0(S),1(P),2(D),3(F (+=L=l1+l2,l1+l2?1,,l1?l2=λ1+λ2,λ1+λ2?1,,λ1?λ2Lz=MLz=MML=∑M=∑ML=L,L?1,,?M= quantumnumberofspinisthesameasthatofJ=L+=+J J(J+ (+J=L+S,L+S?1,,L?=+S,+S?1,? 2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomic2S+1

2S+1 g+++-2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicFilled111gUnfilledThevalueofangularmomentumischaracterizedbythemolecularorbitaloccupiedbytheunpaired2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicTheground-stateconfigurationofoxygenmoleculeisπ M M 20000000102011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicMM10MM102101211SMM102MM1020012103gS3gMM1MM10-200010-01S2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicSelectruleofelectronicS

g

u

g2011-11- 復旦大學化學 物理化學3-13Writetheelectronicconfigurationsandthecorrespondingmoleculartermsofgroundstatesforfollowingspecies:H222222BNF2H222222BNF222N2H2N2

2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicComparisonofVB&MOVB?1212 2 21 11 2M 2M a b B.O.Approximation1212 1 rE(R a b 12One ??2?1? ? +U(1)ψi= Trialψ(1)C1?a(1)C2?bC2?b(1)?A(2) ?a+?b ψ1ψ 2+2S 22S ?a??b ψ1ψ 2?2S 22S2011-11- 復旦大學化學 物理化學

3-3thestructureofdiatomicComparisonofVB& 無2011-11- 復旦大學化學 物理化學Orbital?j=∑?j=∑i??=?sp= n+?s?pf= n+[fs+nf]=p n+ 3nSomepropertiesofhybrid2011-11- 復旦大學化學 物理化學2011-11- 復旦大學化學 αl1?αlαl1?αl∫?k?ld∫?k?ldτ=δαk1?αk

?l s ∫?k?ld

=δ

=0=∫

αks

αls

1?αk1?αlαk α1?αk1?αlαk αl1?αk 1?αl

∫

αkαl1?αkαkαl1?αk1?αl(1?α)(1?ααkαlklcoscosθ=2011-11- 復旦大學化學 物理化學SummaryofHybridOrbitals&Their2011-11- 復旦大學化學 yx物理化學yxsp31434?1 s1434

px

1s 314 314?2

s+Cpx

+Cpypy∫?∫?1?2dτ=∫??2τ= =Cpy112323 1s p12323 2011-11- 復旦大學化學 物理化學141?3141

s+Cpx

+Cpy

+Cpz∫?∫??3τ=∫?2?3dτ=?3?3dτCpx=Cpy=Cz=16?3

1s121

px

py pz?4

1s2

px

py pz121612161211612